Question

It is proposed that future space stations create an artificial gravity by rotating. Suppose a space station is constructed as a 800-m-diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. What rotation period will provide "normal" gravity?

Answer 1

T=56.77s

Step-by-step explanation:

We must use the formula for centripetal acceleration:

`a_(cp)=(v^2)/(r)`

We know the radius r and we want is to obtain a centripetal acceleration equal to g. Since velocity is distance over time, on this circle we can take distance as the circumference (which is of value
`2\pi r`) and thus the time will be the period T because that's the time a point takes to travel the whole circumference, so we can write:

`g=a_(cp)=(v^2)/(r)=(((2\pi r)/(T))^2)/(r)`

or:

`g=(4\pi^2 r)/(T^2)`

and since we want the period:

`T=\sqrt{(4\pi^2 r)/(g)}=2\pi\sqrt{(r)/(g)}`

which for our values is:

`T=2\pi\sqrt{((800m))/((9.8m/s^2))}=56.77s`